WASHINGTON (Reuters) – President Barack Obama sketched an ambitious second-term agenda in his State of the Union speech on Tuesday, challenging a divided Congress to back his proposals to create middle-class jobs and overhaul gun and immigration laws.

Obama entered the well of the House of Representatives for his address to a joint session of Congress at a time when he is again locked in a bitter battle with Republicans over taxes and spending, and this tussle cast a heavy shadow over his appearance.

Americans, said Obama, do not expect government to solve every problem, “but they do expect us to put the nation’s interests before party. They do expect us to forge reasonable compromises where we can.”

But many of his proposals may face a difficult path getting through Congress. He proposed raising the U.S. minimum wage for workers from $7.25 to $9 an hour. Republicans typically oppose increases in the minimum wage out of worry it will prompt businesses to fire workers.

He backed a $50 billion program to fund infrastructure rebuilding projects like fixing aging bridges, but many Republicans are adamantly against such stimulative government spending after Obama’s first term $787 billion stimulus did not lead to a dramatic reversal in the unemployment rate.

“Our economy is adding jobs, but too many people still can’t find full-time employment,” he said. “Corporate profits have rocketed to all-time highs, but for more than a decade, wages and incomes have barely budged.”

It was the kind of rhetoric Obama used to great effect during his re-election campaign when he appealed to the middle class, and he made clear he wanted to help those who supported him, to “reignite the true engine of America’s economic growth, a rising, thriving middle class.”

Seeking to use momentum from his re-election victory, the Democratic president urged Congress to increase taxes on the wealthy, overhaul U.S. immigration laws and enact tighter gun controls. He has about a year to get his legislative priorities enacted before Americans shift attention to 2014 congressional elections.

In a nod to Republican worries over what they see as out-of-control government spending on entitlement programs for the elderly and poor, Obama said he would back efforts to reduce health-care spending by the same amount over a decade as proposed by a bipartisan commission whose recommendations he had rejected.

He outlined steps to unwind U.S. involvement in the unpopular 11-year-old Afghanistan war and plans to announce that 34,000 of the 66,000 U.S. troops still there will return by early 2014.

He did not give details of what sort of residual American presence might remain in Afghanistan after 2014, when the U.S. withdrawal is supposed to be complete.

Obama’s speech came a day after North Korea conducted its third underground test of a nuclear device in response to what it called U.S. hostility.

“Provocations of the sort we saw last night will only isolate them further, as we stand by our allies, strengthen our own missile defense and lead the world in taking firm action in response to these threats,” he said.